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Unformatted text preview:  Standard Error tratio P[T>t]  Mean of X +++++++ Constant .13525584 .07257279 1.864 .0638 LOGY 1.00306313 .00938791 106.846 .0000 7.99083133 ˜˜˜™™ ™ 23/45 Part 15: Generalized Regression Applications FGLS ++  AR(1) Model: e(t) = rho * e(t1) + u(t)   Initial value of rho = .90693  <<<***  Maximum iterations = 100   Method = Prais  Winsten   Iter= 1, SS= .017, LogL= 666.519353   Iter= 2, SS= .017, LogL= 666.573544   Final value of Rho = .910496  <<<***  Iter= 2, SS= .017, LogL= 666.573544   DurbinWatson: e(t) = .179008   Std. Deviation: e(t) = .022308   Std. Deviation: u(t) = .009225   DurbinWatson: u(t) = 2.512611   Autocorrelation: u(t) = .256306   N[0,1] used for significance levels  ++ +++++++ Variable  Coefficient  Standard Error b/St.Er.P[Z>z]  Mean of X +++++++ Constant .08791441 .09678008 .908 .3637 LOGY .99749200 .01208806 82.519 .0000 7.99083133 RHO .91049600 .02902326 31.371 .0000 ˜˜˜™™ ™ 24/45 Part 15: Generalized Regression Applications Seemingly Unrelated Regressions The classical regression model, y i = Xii + i. Applies to each of M equations and T observations. Familiar example: The capital asset pricing model: ( r m  r f) = m i + m( r market – r f ) + m Not quite the same as a panel data model. M is usually small  say 3 or 4. (The CAPM might have M in the thousands, but it is a special case for other reasons.) ˜˜˜™™ ™ 25/45 Part 15: Generalized Regression Applications Formulation Consider an extension of the groupwise heteroscedastic model: We had yi = Xi + i with E[ iX ] = 0, Var[ iX ] = i2 I . Now, allow two extensions: Different coefficient vectors for each group, Correlation across the observations at each specific point in time (think about the CAPM above. Variation in excess returns is affected both by firm specific factors and by the economy as a whole). Stack the equations to obtain a GR model. ˜˜˜™™ ™ 26/45 Part 15: Generalized Regression Applications SUR Model ˜˜˜™™ ™ 27/45 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 2 2 1 2 2 Two Equation System or = + Ε[  ] , Ε[  ] = E = + = + ÷ = + ′ ′ ′ = ′ ′ y Xβ y X β y Xβ y X β y Xβ X X X ε ε ε ε ε ε ε ε ε ε εε ε ε ε ε 11 12 12 22 2 = σ σ = σ σ σ I I I I Ω Part 15: Generalized Regression Applications OLS and GLS Each equation can be fit by OLS ignoring all others. Why do GLS?...
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 Fall '10
 H.Bierens
 Econometrics, Least Squares, Regression Analysis, FGLS, GLS, Regression Applications

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